Lossy Data Decoding via Convex Projection for Lossless Recoding
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Solution Overview
Problem
Conventional decoding methods for lossy compressed data fail to completely restore the original signal and maintain embedded information, particularly when errors occur during clipping or integer-conversion, leading to information loss and inability to guarantee lossless recoding or retention of watermarks.
Innovation Solution
The method employs convex projection techniques by orthogonally projecting vectors between two convex aggregates, X and Y, to iteratively converge on a common solution, ensuring that the decoded signal can be accurately re-encoded and maintaining the structure of the signal within a certain quantization range.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If clipping or integer-conversion is applied to the inversely converted signal, then the signal can be converted into discrete digital data, but information is lost and the original stream cannot be restored
Solution Approach 1:
The patent applies preliminary action by performing convex projection to find an optimal real number vector before the clipping and integer-conversion steps. This pre-processing ensures that the subsequent discrete conversion minimizes information loss and enables accurate restoration of the original stream during re-encoding.
Solution Approach 2:
The patent changes the parameter space by working with real number vectors in a continuous domain before converting to discrete integers. By optimizing the real number vector through convex projection and maintaining it within a convex aggregate, the system preserves more information that can be recovered during re-encoding, effectively transforming the parameter representation to avoid irreversible loss.
2Quantity of substance
If lossy compression is applied to reduce data volume, then compression ratio is improved, but the original signal cannot be accurately reproduced
Solution Approach 1:
The patent changes the parameter representation by using real number vectors instead of directly quantized integers. This allows the system to maintain higher precision in the parameter space during compression, enabling accurate signal reproduction when the data is re-encoded, while still achieving data volume reduction through lossy compression.
Solution Approach 2:
The patent implements a feedback mechanism where the decoded signal is re-encoded and compared with the original coded stream. This feedback loop allows the system to verify that the real number vector maintains the necessary structure for accurate restoration, ensuring that compression does not irreversibly damage the signal.
3Productivity
If conventional decoding methods are used, then decoding speed is maintained, but embedded information such as watermarks is lost
Solution Approach 1:
The patent applies preliminary action by performing convex projection to optimize the real number vector before final conversion. This pre-processing step preserves embedded information such as watermarks by finding a vector that minimizes distortion, allowing conventional fast decoding methods to maintain their speed while the optimized vector ensures information preservation.
Data Source
AI summary
Provided are a program, a method, and an apparatus for decoding coded data, capable of completely restoring an original stream when decoded data is coded again by causing a computer to function as: means for receiving an input of a signal coded by lossy compression and orthogonally projecting an optional real number vector on one convex aggregate X in a first vector space in which the decoded signal is present; means for judging convergence of convex projection and obtaining a real number vector x belonging to the aggregate X to output the same as a decoded signal when the convergence of the convex projection is judged; and means for orthogonally projecting an optional vector of the first vector space on one convex aggregate Y in a second vector space different from the first vector space when the convergence of the convex projection is not judged, and then repeating orthogonal projection on the aggregate X and the aggregate Y with the coded signal set as an initial value.